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Fractal geometry : mathematical foundations and applications / / Kenneth Falconer
| Fractal geometry : mathematical foundations and applications / / Kenneth Falconer |
| Autore | Falconer K. J. <1952-> |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Hoboken : , : John Wiley & Sons, , 2014 |
| Descrizione fisica | 1 online resource (400 p.) |
| Disciplina | 514/.742 |
| Soggetto topico |
Fractals
Dimension theory (Topology) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-76286-X
1-118-76285-1 |
| Classificazione | MAT031000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Contents; Preface to the first edition; Preface to the second edition; Preface to the third edition; Course suggestions; Introduction; Part I Foundations; Chapter 1 Mathematical background; 1.1 Basic set theory; 1.2 Functions and limits; 1.3 Measures and mass distributions; 1.4 Notes on probability theory; 1.5 Notes and references; Exercises; Chapter 2 Box-counting dimension; 2.1 Box-counting dimensions; 2.2 Properties and problems of box-counting dimension; 2.3 Modified box-counting dimensions; 2.4 Some other definitions of dimension; 2.5 Notes and references
ExercisesChapter 3 Hausdorff and packing measures and dimensions; 3.1 Hausdorff measure; 3.2 Hausdorff dimension; 3.3 Calculation of Hausdorff dimension-simple examples; 3.4 Equivalent definitions of Hausdorff dimension; 3.5 Packing measure and dimensions; 3.6 Finer definitions of dimension; 3.7 Dimension prints; 3.8 Porosity; 3.9 Notes and references; Exercises; Chapter 4 Techniques for calculating dimensions; 4.1 Basic methods; 4.2 Subsets of finite measure; 4.3 Potential theoretic methods; 4.4 Fourier transform methods; 4.5 Notes and references; Exercises Chapter 5 Local structure of fractals5.1 Densities; 5.2 Structure of 1-sets; 5.3 Tangents to s-sets; 5.4 Notes and references; Exercises; Chapter 6 Projections of fractals; 6.1 Projections of arbitrary sets; 6.2 Projections of s-sets of integral dimension; 6.3 Projections of arbitrary sets of integral dimension; 6.4 Notes and references; Exercises; Chapter 7 Products of fractals; 7.1 Product formulae; 7.2 Notes and references; Exercises; Chapter 8 Intersections of fractals; 8.1 Intersection formulae for fractals; 8.2 Sets with large intersection; 8.3 Notes and references; Exercises Part II Applications and ExamplesChapter 9 Iterated function systems-self-similar and self-affine sets; 9.1 Iterated function systems; 9.2 Dimensions of self-similar sets; 9.3 Some variations; 9.4 Self-affine sets; 9.5 Applications to encoding images; 9.6 Zeta functions and complex dimensions; 9.7 Notes and references; Exercises; Chapter 10 Examples from number theory; 10.1 Distribution of digits of numbers; 10.2 Continued fractions; 10.3 Diophantine approximation; 10.4 Notes and references; Exercises; Chapter 11 Graphs of functions; 11.1 Dimensions of graphs 11.2 Autocorrelation of fractal functions11.3 Notes and references; Exercises; Chapter 12 Examples from pure mathematics; 12.1 Duality and the Kakeya problem; 12.2 Vitushkin's conjecture; 12.3 Convex functions; 12.4 Fractal groups and rings; 12.5 Notes and references; Exercises; Chapter 13 Dynamical systems; 13.1 Repellers and iterated function systems; 13.2 The logistic map; 13.3 Stretching and folding transformations; 13.4 The solenoid; 13.5 Continuous dynamical systems; 13.6 Small divisor theory; 13.7 Lyapunov exponents and entropies; 13.8 Notes and references; Exercises Chapter 14 Iteration of complex functions-Julia sets and the Mandelbrot set |
| Record Nr. | UNINA-9910453807903321 |
Falconer K. J. <1952->
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| Hoboken : , : John Wiley & Sons, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Quantum dynamics for classical systems [[electronic resource] ] : with applications of the number operator / / Fabio Bagarello
| Quantum dynamics for classical systems [[electronic resource] ] : with applications of the number operator / / Fabio Bagarello |
| Autore | Bagarello Fabio <1964-> |
| Pubbl/distr/stampa | Hoboken, : Wiley, 2013 |
| Descrizione fisica | 1 online resource (203 pages) : illustrations, graphs |
| Disciplina | 300.1/53012 |
| Soggetto topico |
Social sciences - Mathematics
Business mathematics Quantum theory - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-40059-3
1-118-40058-5 1-283-66504-2 1-118-40060-7 |
| Classificazione | MAT031000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910208835703321 |
|
Bagarello Fabio <1964->
|
||
| Hoboken, : Wiley, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Quantum dynamics for classical systems : with applications of the number operator / / Fabio Bagarello
| Quantum dynamics for classical systems : with applications of the number operator / / Fabio Bagarello |
| Autore | Bagarello Fabio <1964-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, : Wiley, 2013 |
| Descrizione fisica | 1 online resource (203 pages) : illustrations, graphs |
| Disciplina | 300.1/53012 |
| Soggetto topico |
Social sciences - Mathematics
Business mathematics Quantum theory - Mathematics |
| ISBN |
1-118-40059-3
1-118-40058-5 1-283-66504-2 1-118-40060-7 |
| Classificazione | MAT031000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- QUANTUM DYNAMICS FOR CLASSICAL SYSTEMS -- CONTENTS -- PREFACE -- ACKNOWLEDGMENTS -- 1 WHY A QUANTUM TOOL IN CLASSICAL CONTEXTS? -- 1.1 A First View of (Anti-)Commutation Rules -- 1.2 Our Point of View -- 1.3 Do Not Worry About Heisenberg! -- 1.4 Other Appearances of Quantum Mechanics in Classical Problems -- 1.5 Organization of the Book -- 2 SOME PRELIMINARIES -- 2.1 The Bosonic Number Operator -- 2.2 The Fermionic Number Operator -- 2.3 Dynamics for a Quantum System -- 2.3.1 Schrödinger Representation -- 2.3.2 Heisenberg Representation -- 2.3.3 Interaction Representation -- 2.4 Heisenberg Uncertainty Principle -- 2.5 Some Perturbation Schemes in Quantum Mechanics -- 2.5.1 A Time-Dependent Point of View -- 2.5.2 Feynman Graphs -- 2.5.3 Dyson's Perturbation Theory -- 2.5.4 The Stochastic Limit -- 2.6 Few Words on States -- 2.7 Getting an Exponential Law from a Hamiltonian -- 2.7.1 Non-Self-Adjoint Hamiltonians for Damping -- 2.8 Green's Function -- I SYSTEMS WITH FEW ACTORS -- 3 LOVE AFFAIRS -- 3.1 Introduction and Preliminaries -- 3.2 The First Model -- 3.2.1 Numerical Results for M > -- 1 -- 3.3 A Love Triangle -- 3.3.1 Another Generalization -- 3.4 Damped Love Affairs -- 3.4.1 Some Plots -- 3.5 Comparison with Other Strategies -- 4 MIGRATION AND INTERACTION BETWEEN SPECIES -- 4.1 Introduction and Preliminaries -- 4.2 A First Model -- 4.3 A Spatial Model -- 4.3.1 A Simple Case: Equal Coefficients -- 4.3.2 Back to the General Case: Migration -- 4.4 The Role of a Reservoir -- 4.5 Competition Between Populations -- 4.6 Further Comments -- 5 LEVELS OF WELFARE: THE ROLE OF RESERVOIRS -- 5.1 The Model -- 5.2 The Small l Regime -- 5.2.1 The Sub-Closed System -- 5.2.2 And Now, the Reservoirs! -- 5.3 Back to S -- 5.3.1 What If M = 2? -- 5.4 Final Comments -- 6 AN INTERLUDE: WRITING THE HAMILTONIAN -- 6.1 Closed Systems -- 6.2 Open Systems.
6.3 Generalizations -- II SYSTEMS WITH MANY ACTORS -- 7 A FIRST LOOK AT STOCK MARKETS -- 7.1 An Introductory Model -- 8 ALL-IN-ONE MODELS -- 8.1 The Genesis of the Model -- 8.1.1 The Effective Hamiltonian -- 8.2 A Two-Traders Model -- 8.2.1 An Interlude: the Definition of cP -- 8.2.2 Back to the Model -- 8.3 Many Traders -- 8.3.1 The Stochastic Limit of the Model -- 8.3.2 The FPL Approximation -- 9 MODELS WITH AN EXTERNAL FIELD -- 9.1 The Mixed Model -- 9.1.1 Interpretation of the Parameters -- 9.2 A Time-Dependent Point of View -- 9.2.1 First-Order Corrections -- 9.2.2 Second-Order Corrections -- 9.2.3 Feynman Graphs -- 9.3 Final Considerations -- 10 CONCLUSIONS -- 10.1 Other Possible Number Operators -- 10.1.1 Pauli Matrices -- 10.1.2 Pseudobosons -- 10.1.3 Nonlinear Pseudobosons -- 10.1.4 Algebra for an M + 1 Level System -- 10.2 What Else? -- BIBLIOGRAPHY -- INDEX. |
| Record Nr. | UNINA-9910810225403321 |
|
Bagarello Fabio <1964->
|
||
| Hoboken, : Wiley, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||